Calculating Series System Reliability and Reliability for Each Individual Component

[jag53]

Hi,

I am currently trying to calculate the reliability for a certain system. I have obtained the formula for a series system (which is what I have), but how do you calculate the reliability for each individual component within the system?

Also, I have obtained several MTBF figures for several components. Given these numbers is there a way to calculate a MTBF for the system as a whole?

It needs to be proven that this system will last for 10 years with little or no preventative maintanence. If I have this correct calculating the reliability will give me the probability the the system will operate correctly and the MTBF will give the average hours before it fails.

I basically need some direction on how determine system reliabiliy or MTBF. Any help will do!

Thanks,

jag53

[Brian Myers]

MTBF = 1 / lambda

(lambda is a variable equal to the failure rate)

Rt = Reliability = e^[-(lambda)*time]

SO...

if you have the MTBF for all of your components you can easily calculate the Rt (Reliability wrt time) for each component. Plug those calculated Rt numbers into your system formula (Rt1 * Rt2 * Rt3 ... = Rtsys) and you can calculate the Rt for the system. From there your can figure out the MTBF for the system.

By the way, is this system repairable? If not, you should refer to MTBF (Mean Time BETWEEN Failures) as MTTF (Mean Time TO Failure).

Brian

[jag53]

Thank you Brian

In the equation for reliability, time is referring to which time? If I want to see how reliable my system will be in ten years, is this where I enter it?

Thanks,
jag53

[psavijay]

Hi

Attached is what we are doing as MTTR and MTBF for Machine maintenance, as per my understanding it can be extended in to sub systems if requires (series of sub components)

There are 2 different areas Machine Reliability for maintenance monitoring and comparision with Manufacturer reliability assurance, and Product reliability.

Attached is for Machine maintenance in simpleway.

Based on this data we can do Reliability predictions for Future (over a period of time)

Regards
A.Vijayakumar

[Michael Walmsley]

Several key points have been highlighted and some questions need be answered .

1) Is it deemed a repairable system?
2) How complex is the system?
3) What are you contractually held to?
4) Is there significant product liability / safety concerns associated with it?

If not 1) then the thing you need to key in on is MTTF , not MTBF
where
MTTF (Mean time to failure).

Under the MTBF scenario,many assume exponentiality as the distribution for the failures and utilize either the DUANE or AMSAA models to model growth.

Under MTTF scenario , exponentiality may be out along with the DUANE model.

With the MTTF approach , you assume nothing with respect to the underlying
failure distribution. It is what it is. You necessarily have to have some historical test to failure data (and enough of it) to analyze and determine what the underlying failure distribution is . It could be Normal , Weibull , Rayleigh , LogNormal ,....
OR
You may opt to perform degradation analysis against a key performance requirement in lieu of test to failure data and determine what the underlying distribution is within the region of interest, "against" time.

For a serial system, Reliability is related to the "minimum time to failure distribution" for failure modes.
eg for all the failure modes tested against , which one happens first on the time axis. This is your "weakest point in the chain".

When doing degradation analysis , against several key performance criteria for a given product , the weakest point in the chain will be related to that area in performance which degrades the quickest.

Reliability Assurance is non-trivial. Especially from a product liability and safety standpoint. You cannot assume exponentiality to make the mathematics easy.

If you have enough data is the key point ( 5 - 15 data points per failure mode or performance requirement). Without it you cannot model anything.